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Efficient sampling from the Boltzmann distribution given its energy function is a key challenge for modeling complex physical systems such as molecules. Boltzmann Generators address this problem by leveraging continuous normalizing flows to…

Machine Learning · Computer Science 2025-10-17 Rishal Aggarwal , Jacky Chen , Nicholas M. Boffi , David Ryan Koes

While generative modeling has achieved remarkable success on tasks like natural language-conditioned image generation, enabling model adaptation from example data points remains a relatively underexplored and challenging problem. To this…

Machine Learning · Computer Science 2026-05-08 Tyler Ingebrand , Ruihan Zhao , Kushagra Gupta , David Fridovich-Keil , Sandeep P. Chinchali , Ufuk Topcu

Flows are exact-likelihood generative neural networks that transform samples from a simple prior distribution to the samples of the probability distribution of interest. Boltzmann Generators (BG) combine flows and statistical mechanics to…

Machine Learning · Statistics 2019-10-03 Jonas Köhler , Leon Klein , Frank Noé

This paper investigates energy guidance in generative modeling, where the target distribution is defined as $q(\mathbf x) \propto p(\mathbf x)\exp(-\beta \mathcal E(\mathbf x))$, with $p(\mathbf x)$ being the data distribution and $\mathcal…

Machine Learning · Computer Science 2025-03-10 Shiyuan Zhang , Weitong Zhang , Quanquan Gu

The task of conditional generation is one of the most important applications of generative models, and numerous methods have been developed to date based on the celebrated flow-based models. However, many flow-based models in use today are…

Machine Learning · Computer Science 2024-07-08 Noboru Isobe , Masanori Koyama , Jinzhe Zhang , Kohei Hayashi , Kenji Fukumizu

Sampling from unnormalized densities is analogous to the generative modeling problem, but the target distribution is defined by a known energy function instead of data samples. Because evaluating the energy function is often costly, a…

Machine Learning · Computer Science 2026-05-06 Aaron Havens , Brian Karrer , Neta Shaul

Sampling molecular conformations from the Boltzmann distribution is essential for computational chemistry, but iterative diffusion methods are prohibitively slow. Drifting Models offer one-step generation, yet their equilibrium matches the…

Chemical Physics · Physics 2026-03-09 Pipi Hu

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently…

Machine Learning · Computer Science 2024-02-27 Ricky T. Q. Chen , Yaron Lipman

Normalizing Flows (NFs) are widely used in deep generative models for their exact likelihood estimation and efficient sampling. However, they require substantial memory since the latent space matches the input dimension. Multi-scale…

Machine Learning · Computer Science 2025-12-11 Wei Chen , Shian Du , Shigui Li , Delu Zeng , John Paisley

Conditional flow matching (CFM) stands out as an efficient, simulation-free approach for training flow-based generative models, achieving remarkable performance for data generation. However, CFM is insufficient to ensure accuracy in…

Machine Learning · Computer Science 2026-02-03 Yuhao Huang , Taos Transue , Shih-Hsin Wang , William Feldman , Hong Zhang , Bao Wang

Forecasting state evolution of network systems, such as the spread of information on social networks, is significant for effective policy interventions and resource management. However, the underlying propagation dynamics constantly shift…

Computational Engineering, Finance, and Science · Computer Science 2025-10-13 Shihe Zhou , Ruikun Li , Huandong Wang , Yong Li

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for…

Machine Learning · Computer Science 2023-02-09 Yaron Lipman , Ricky T. Q. Chen , Heli Ben-Hamu , Maximilian Nickel , Matt Le

Modeling complex systems that evolve toward equilibrium distributions is important in various physical applications, including molecular dynamics and robotic control. These systems often follow the stochastic gradient descent of an…

Machine Learning · Computer Science 2024-10-16 Christopher Iliffe Sprague , Arne Elofsson , Hossein Azizpour

Forecasting conditional stochastic nonlinear dynamical systems is a fundamental challenge repeatedly encountered across the biological and physical sciences. While flow-based models can impressively predict the temporal evolution of…

Machine Learning · Computer Science 2025-04-02 Adam P. Generale , Andreas E. Robertson , Surya R. Kalidindi

Deep generative models provide state-of-the-art performance across a wide array of applications, with recent studies showing increasing applicability for science and engineering. Despite a growing corpus of literature focused on the…

Machine Learning · Computer Science 2026-05-14 Jacob K. Christopher , James E. Warner , Ferdinando Fioretto

The generation of equilibrium samples of molecular systems has been a long-standing problem in statistical physics. Boltzmann Generators are a generative machine learning method that addresses this issue by learning a transformation via a…

Machine Learning · Statistics 2025-02-04 Leon Klein , Frank Noé

Energy-Based Models (EBMs) have proven to be a highly effective approach for modelling densities on finite-dimensional spaces. Their ability to incorporate domain-specific choices and constraints into the structure of the model through…

Machine Learning · Computer Science 2023-02-24 Jen Ning Lim , Sebastian Vollmer , Lorenz Wolf , Andrew Duncan

Distribution-to-distribution generative models support scientific imaging tasks ranging from modeling cellular perturbation responses to translating medical images across conditions. Trustworthy generation requires reliability, or…

Machine Learning · Computer Science 2026-05-22 Dongxia Wu , Yuhui Zhang , Serena Yeung-Levy , Emma Lundberg , Emily B. Fox

Deep generative models have recently been applied to physical systems governed by partial differential equations (PDEs), offering scalable simulation and uncertainty-aware inference. However, enforcing physical constraints, such as…

Machine Learning · Computer Science 2025-11-27 Utkarsh Utkarsh , Pengfei Cai , Alan Edelman , Rafael Gomez-Bombarelli , Christopher Vincent Rackauckas

The Boltzmann distribution of a protein provides a roadmap to all of its functional states. Normalizing flows are a promising tool for modeling this distribution, but current methods are intractable for typical pharmacological targets; they…

Machine Learning · Computer Science 2024-01-10 Joseph C. Kim , David Bloore , Karan Kapoor , Jun Feng , Ming-Hong Hao , Mengdi Wang